Theoretical research on networks: models and methodology

This note is based on my invited talk at the 4th Intl. Colloq. on Structural Information and Communication Complexity (SIROCCO'97). In it, I discuss a few \meta-issues" concerning theoretical research on networks, and I illustrate these issues with some recent research of mine (so that all critical remarks can be focused in my direction). My central foci are the selection of problems and models, and the tools for studying them. Technology-focused theoretical computer scientists work in a strange laboratory. On the one hand, the tools they work with are supplied by the eld of mathematics. On the other hand, the objects that they work on come from a very diierent constituency, the practitioners in the areas of computer and communication technology. Researchers in this area face a tantalizing temptation to cleave to the elegance-seeking paradigm of mathematics in their work|at the risk of producing results that apply only in a gedanken universe. My intention is to describe here some of the dangers that I see in our research world and to suggest, via examples, ways to avoid some of these dangers. I choose my exemplary studies just from my own work (with valued collaborators) so that any criticism that may be engendered by my thesis will be directed solely at me. I begin my remarks with two research-oriented questions that I view as among the most important that a theoretician can ask|for only a theoretician can ask them. What really matters? This question really encapsulates the power of the theoretical researcher's ability to abstract from the details of current technology. It allows the researcher to question what